1. Field of the Invention
The present invention relates to a finite element modeling method and a storage medium used in a process of finite element analysis and, more particularly, to a hexahedral finite element modeling method for controlling the element size and a storage medium used in the process of finite element analysis, the method and storage medium designed to more effectively model a hexahedral finite element by sequentially meshing the element into face-refined transition unit mesh module, edge-refined transition unit mesh module and vertex-refined transition unit mesh module.
2. Description of the Prior Art
A finite element method (FEM), which is one of the approximation numerical analyses of differential equations, has been preferably used in some engineering research fields, such as a mechanical engineering field, concentrating upon the mechanical analysis of a target system.
Such an FEM has been typically used in strength and strain analysis of a variety of machines and structures, fluid flow analysis, and electromagnetic field analysis. In order to perform an FEM for mechanically analyzing a target system, such as a machine or a structure, the problem domain of the target system is primarily divided into several sections having unit volumes. That is, the problem domain is divided into finite element meshes. In such a case, the problem domain is a target area of the system to be mechanically analyzed through the FEM.
Such a division of the problem domain into finite element meshes is so-called “a finite element modeling” in the field. The finite element modeling determines the accuracy in the prediction of the mechanical behavior of the target system.
The conventional FEM has been typically carried out through three steps: a pre-processor step, a solver step, and a post-processor step. Of the three steps, the solver step is a numerical calculation step.
At the pre-processor step, an ideal modeling process for a target system is performed while excluding the variables of environmental interest prior to sequentially performing a geometrical modeling process and a finite element modeling process.
In the finite element modeling process, it is necessary to primarily set the problem domain of a target system and divide the problem domain into several sections having a predetermined shape and various unit volumes, thus producing finite element meshes.
A finite element mesh consists of an element having a unit volume, and a plurality of nodes positioned at the vertexes of the element.
In the conventional FEM, the finite elements are classified into several types, for example, tetrahedral elements, hexahedral elements, pyramid elements, etc., in accordance with their shapes. Of the above-mentioned finite elements, the tetrahedral elements and hexahedral elements have been more preferably and frequently used in the FEM.
During a finite element analysis performed through the finite element modeling process, it is necessary to appropriately control the face density or node density of an element mesh in accordance with expected stress, deformation and strain generated in a target system in response to impact applied to the system.
That is, an area of the finite element, corresponding to an area of the target system expected to generate small calculation error during an engineering calculation process, is preferably divided into relatively larger meshes such that the meshed element has a low face density or low node density at the area. On the other hand, another area of the finite element, corresponding to an area of the target system expected to generate large calculation error during the engineering calculation process, is preferably divided into relatively smaller meshes such that the meshed element has a high face density or high node density. When the finite element is divided into meshes having different densities as described above, it is possible to get desired high precision of the FEM even if the FEM is carried out with the conventional computational complexity.
FIG. 1 is a flowchart of a hexahedral finite element modeling method according to the prior art. FIG. 2 is a perspective view of a hexahedral finite element mesh generated through the conventional hexahedral finite element modeling method.
As shown in the drawings, the conventional hexahedral finite element 1 has six faces, twelve edges and four nodes.
In the hexahedral finite element 1, it is necessary to reduce the face density and node density at an area of the element expected to generate small calculation error during a numerical calculation process as described above. Such an area is thus divided into relatively larger element meshes. In the conventional FEM, each of three faces of the finite element 1, having a first node in common, is divided into four uniform sections at step S10 of FIG. 1. Therefore, the face density and node density of the three faces are increased.
Thereafter, each of another three faces, commonly having a second node diagonally opposite to the first node, is divided into four uniform sections at step S20.
At step S30, each of the three faces, commonly having the second node and primarily divided into four sections at step S20, is secondarily divided into four uniform sections at a predetermined square area around the second node, and so the square areas are uniformly divided into twelve uniform faces concentrated at the second node diagonally opposite to the first node.
The square areas, having the uniformly divided twelve faces, are the areas of the finite element 1 expected to generate large calculation error during an engineering calculation process. Therefore, the areas are divided into relatively smaller meshes such that the meshed element 1 has a high face density and a high node density at said areas.
However, the conventional finite element modeling method is problematic as follows:
First, the conventional finite element modeling method is problematic in that it is almost impossible to accomplish desired complete connectivity between the densely meshed areas and sparsely meshed areas of a finite element during the process of modeling a target system in the form of hexahedral finite element by differentially meshing the element.
Second, even when the hexahedral finite element is differentially meshed in consideration of different calculation errors and different face and node densities caused by the errors, the difference in the face and node densities between the densely meshed and sparsely meshed areas of the element exceeds a reasonable limit. Therefore, the conventional finite element modeling method cannot accomplish a desired uniform size ratio of finite elements.